February 11, 2008

What use is sources-of-growth accounting?

I am teaching this stuff this week, and while I enjoy doing it and think it is important for students to know--no World Bank country economic memorandum is apparently complete without a sources-of-growth exercise--I wonder what purpose it really serves.

These accounting exercises come in two flavors. A levels-exercise which decomposes differences in GDP per worker across countries into factor endowments and efficiency (or TFP). For the state of the art on this, see this paper by Francesco Caselli. The more traditional kind decomposes growth within a country into components having to do with physical and human capital deepening and a residual (TFP growth). A comprehensive source on the latter is the 2003 paper by Barry Bosworth and Susan Collins.

Aside from all kind of measurement problems, these accounting exercises say nothing about causality, and so are very hard to interpret. Say you found it's 50% efficiency and 50% factor endowments. What conclusion do you draw from it? You could imagine a story where the underlying cause of growth is factor accumulation, with technological upgrading or enhanced allocative efficiency as the by-product. Or you could imagine a story whereby technological change is the driver behind increased accumulation. Both are compatible with the result from accounting decomposition. Indeed, I have yet to see a sources-of-growth decomposition which answers a useful and relevant economic or policy question.

Caselli says that these accounting exercises are just a diagnostic tool--but he does not say how they help us diagnose anything in particular. Sure, they tell us that accumulation alone cannot be the whole story, but is that a surprise to anyone?

Perhaps the best known paper on sources of growth was the Alwyn Young exercise on East Asia, which showed that most of growth was "accounted" for by accumulation rather than productivity growth. In other words, the East Asian miracle was mostly perspiration, and not much inspiration. Yet surely it was a miracle for these countries to have engineered jumps in their investment rates of the order of 20 or more percentage points, and even if the Young decomposition is right (it has been challenged by Chang-Tai Hsieh among others), I am not sure the result teaches us anything of importance. Do you suddenly think less of East Asians because the residual is lower than what you may have anticipated?

So here is a contest for economist (or wannabe economist) readers of this blog: can you come up with an interesting question to which a sources-of-growth decomposition is the answer?

Lets take the Young scenario. If the TFP portion of the growth account had been larger, it would have suggested that the East Asian growth rate can be sustained for a longer time than otherwise. The fact (assume it was not disputed) that TFP accounted for a small portion suggested (correctly) that "one time effects" of capital formation, albeit miraculous, would end rather than be sustained (Stein's law ;-).

Does this kind of reasoning not qualify as diagnostic of the sustainability of long term growth?

I always found one result of that literature very important. Irrespective of what are the underlying causal mechanisms, if you assume that technology is the same across countries, you end up over predicting output per capita in poor countries, the most, the poorer the country. This is not a trivial result. Perhaps it is not surprising, but most of the applied work is not expected to be surprising. See, when it is surprising, it is often dismissed as not being based on well grounded theory.

Based on my experience in a consumer-goods company, which I won't argue (just now) scales to the practice you are considering, it was most valuable when done first beforehand -- a key assumption-surfacing step in the planning process -- and then ex post. This enabled us to prepare plans that had a hypothetical rationale, and then learn from the outcomes. I suspect that a lot of the value depends on the "chart of accounts" or alternative classifications (activity-based or project-based, e.g.) that one uses.

I agree that it doesn't tell us much about "causes," but I think it can be useful for helping us figure out what questions to ask. One recent example I found interesting was the Jorgenson, Ho and Stiroh "Retrospective Look at the US Productivity Growth Resurgence" which showed that the 1995-2005 increase in US productivity growth was mainly due to IT in the first five years, but more broadly-based in the second half. That doesn't tell us why, but it can help us start thinking about what is going on (unless we think its all hopelessly mis-measured).

Maybe growth accounting is more relevant for high-income countries than developing ones. If we think big institutional changes in developing countries might simultaneously improve productivity and incentives for investment, the growth accounting isn't as informative for those cases.

I think you are spot on amselly!! We could even add a whole list of reasons why the profession should have left this growth accounting a long time ago (probably by the time Solow did that 1955 exercise)...

Professor Rodrik, I think growth accounting is something that will embarrass us all at some point (when? I don't really know because I'm surprised it didn't really happen yet)...

"Done correctly", growth accounting will always yield a pointless series for the residual, a bit like a white noise. How to do it correctly? One doesn't need to estimate any elasticities, because we know the shares for a fact already... the equation that constitutes the regression can be arithmetically devised from an accounting IDENTITY... more, any production function can be devised from the same accounting identity (so much for testing the null hypothesis no?)... the implications of this are difficult to underestimate, but just think of those attempts to prove that an economy can be mimicked by a Cobb-Douglas, and how glad and relieved the researcher is when he finds that the elasticities are close to the factor shares (he can then move along and use the TFP series for something else). How could they not be similar? These arguments are not new...

I really like to read your papers and books Professor Rodrik, and the only point that puts me off is, every now and then, some reference to TFPs...

Growth accounting? TFP? Aggregate Production Functions? Still there???? The problem is substantially worse than Dani Rodrik notes, although he is in the right direction. Growth accounting exercises need the assumption that an aggregate production function exists. The aggregation literature told us decades ago that this is not true. When is the profession going to learn this? The problem is different: how can we interpret growth accouting exercises (and econometric estimations of aggregate production functions) if we know that they are not telling us anything at all, because they depend on (or use) "something" that does not exsit? The explantion is that these exercises (and the calcualtion of TFP) are a tautology, a manipulation of the NIPA. There is no sound theory behind them.

The purpose of growth accounting is quite simple: ACCOUNTING --- NOT MODELING.

Accounting requires a framework, and that's what the neoclassical 1957 Solow framework offers.

Growth accounting serves the purpose of classifying growth into that part that can be traced to measured inputs and that part which cannot. The residual can be thought of as a "measure of our ignorance", that part for which we were not able to find measured or measurable inputs. The more sizable the residual, the more humble we ought to be about the accounting exercise.

Sure, it's all within a framework. Some readers here reject the framework. What's your alternative, Karl?

Prof. Rodrik asks:

1) "Say you found it's 50% efficiency and 50% factor endowments. What conclusion do you draw from it?"

@ You can conclude that you've only done half the job. You may want to look into the work of Denison, Jorgenson, Mankiw, Romer, and Weil, Barro, and others who have seriously looked into expanding the range of measured inputs.

2) "You could imagine a story where the underlying cause of growth is factor accumulation, with technological upgrading or enhanced allocative efficiency as the by-product. Or you could imagine a story whereby technological change is the driver behind increased accumulation. Both are compatible with the result from accounting decomposition."

@ Sure, that's where you want to move away from accounting and towards modeling. Solow's 1956 model was a first shot, which typically explains about half of the growth. A lot more work has been done since. The new growth theories of Romer, Lucas, Aghion and Howitt, Grossman and Helpman, the barriers to riches theories of Prescott and Parente, and others, are one giant step in the right direction.

3) "Do you suddenly think less of East Asians because the residual is lower than what you may have anticipated?"

@ To identify the residual with something morally good is very odd. If the residual is a measure of our ignorance I would have thought that the less of it the better. East Asia is a growth accountant's dream come true. Growth accountants love East Asia.

Add the insights from evolutionary theory to show that growth accounting is pointless:

Nelson (1981): it may be fruitful to consider the several sources of growth as being like the inputs into a cake. All are needed. Where complementarity is important, it makes little sense to try to divide up the credit for growth, treating the factors as if they were not complements."

In econometric language: GDP, physical capital, human capital, institutions etc. are all cointegrated with each other.

Angus: Quite the opposite. I did not mean to overload the comment with my own work. But please take a quick look and you will see that the point of these papers is to dismiss a body of literature that relies on a concept without any theorerical foundation, namely, the aggregate production function. Regards

I very much like the comments of ptoche above. The objective of growth accounting is to minimize the residual (ie: to *account* for growth).

It is very unfortunate that words like "technology", "productivity" and "TFP" have become associated with an unexplained residual (*unaccounted* growth).

"TFP" should never be uttered. It just leads to misconceptions such as that of Arun Garg above: that growth is more sustainable (or "better") if it comes from "TFP".

This is not true at all, and wouldn't be even if TFP wasn't a bollocks concept to begin with. Asia's growth miracle was (simplistically) the result of significant relative backwardness combined with good policy reforms. Those reforms stimulated the extremely rapid accumulation of capital. Capital accumulation may not be sustainable at that rate, but continued reform is. Of course each reform needs to be different from the previous or else it isn't reform. The point is that while capital is relatively the scarcest resource, good reforms will focus on encouraging its accumulation. Once something else becomes a binding constraint (Danni, take note ;) good reforms will focus on that, and the Solow-Swan model will not account for the resulting growth.

Dani, if you're teaching a course on this, as someone who did such a course a couple of years ago, I implore you never to use the word "TFP" except to point out that its a load of bollocks. Otherwise you'll just confuse everyone.

Incidentally, frontier models are quite nice for this sort of thing. They are usually used to measure firm level efficiency, but they can be adapted for use at an aggregate level.

They set up the normal (or best practice if you want) growth accounting framework, but instead of leaving the residual unexplained, they then make the residual a function of various things which might be expected to reduce efficiency.

What we can learn from Alwyn Young's work on East Asia is that the author doesn't much like the food they eat, or otherwise care for 'em. The conclusion Young draws is that these countries are still inferior to the west.

If you read the paper carefully, you'll see it's actually one long joke. It's a brilliant paper, though, really -- a true piece of art. He starts off in the introduction thanking "the governments of Korea, Taiwan, Singapore, and Hong Kong for providing reams of never published material and for their kind support and help in clarifying the data" yet he forgets to cite the data in his original chart. If you read carefully, the reason he didn't cite all of the data in that chart is b/c he's made some of it up. (The JPE's editorial standards apparently don't require citing questionable data -- Economists' fetish for numbers is so intense that no one cares from whence they come.) The key to Young's thesis is that Singapore, for example, increased labor force participation by 90% in 25 years. Or, cut off the change between 1980&1990, when Singapore's Census methodology was constant, the lbf increased about 78% from 1965-1980. Turns out, there was no census in Singapore in the mid 1960s. So how did brother Young get his starting data point? First he compared the 1970 & 80 census, even though they differed in methodology, registering nearly a 50% increase. Then, although he doesn't say it in the paper, he did a linear extrapolation back the last five years to knock it up to a 78% increase for the 15 year period! (of course, doing the linear extrapolating back to 1950, nobody was working...) Young's work is rife with these kinds of shenanigans -- this is how he concludes, in his later paper, that growth in China from 1978-98 -- a period of growth perhaps unprecedented in the whole of human history -- that the People's Republic likely had negative productivity growth. To his credit, in his later paper he mischieveously concedes that "with minimal sleight of hand, it is possible to transform any country's growth experience from the extraordinary, to the mundane."

I very much agree with Rodrik that the emphasis on growth accounting within the profession has been misplaced. If I want to look for a growth accounting paper on east asia, i can get several hundred hits. If I want a paper which explains why the East Asian countries grew, however, I almost need to go to a different discipline. Economists have pretty much just decided not to seriously touch it.

i.e.: "If the residual is a measure of our ignorance I would have thought that the less of it the better. East Asia is a growth accountant's dream come true. Growth accountants love East Asia."

Nope. It's not a good thing if your entire increase in output was caused by, say, an increase in labor. You want output per unit of input to increase. Inputs are capital & labor. If increases come only, from, say, more hours worked or more machines than you're probably no better off than before.

although i didn't mind that comment. it was stuff like this:
"The new growth theories of Romer, Lucas, Aghion and Howitt, Grossman and Helpman, the barriers to riches theories of Prescott and Parente, and others, are one giant step in the right direction."

what did u learn from these "new growth theories"? What? Spell it out! I want to know!

Re: "I always found one result of that literature very important. Irrespective of what are the underlying causal mechanisms, if you assume that technology is the same across countries, you end up over predicting output per capita in poor countries, the most, the poorer the country. This is not a trivial result. Perhaps it is not surprising,"

Re: "Lets take the Young scenario. If the TFP portion of the growth account had been larger, it would have suggested that the East Asian growth rate can be sustained for a longer time than otherwise. The fact (assume it was not disputed) that TFP accounted for a small portion suggested (correctly) that "one time effects" of capital formation, albeit miraculous, would end rather than be sustained (Stein's law ;-).

Does this kind of reasoning not qualify as diagnostic of the sustainability of long term growth?

Your reasoning sounds to me backwards. If the Asian Tigers didn't have TFP growth, like Young speculates, then they still should be able to have fast TFP growth in the future (particularly now with their well-educated workforce) according to standard convergence doctrine.

If, on the other hand, they've already pretty much caught up in TFP, then there's not much left they can do -- they've converged. Young says they haven't converged. In Young's mind, though, they probably can't (being as they are populated by yellow people).

Re: "Asia's growth miracle was (simplistically) the result of significant relative backwardness combined with good policy reforms. Those reforms stimulated the extremely rapid accumulation of capital."

Just curious which reforms you think were key. Economic and industrial policies were quite different in each of the East Asian NICs, of course.

Well to take the case that I'm most familiar with (China), the key reform was allowing peasant farmers to keep and/or sell their surpluss (above government mandated production) output.

This kicked off China's growth and a steady 2 decades of good reform has kept it going.

An earlier example of a good reform in China, was ending the great leap forward. If it weren't for that reform, China certainly wouldn't have the population problem it has now.

If you feel that "Asia's growth miracle" refers to Japan, Taiwan, Korea etc. and by taling about China I'm begging the question, well I'm not as familiar with the details of the development histories of those countries. Perhaps I'm guilty of drawing general conclusions from specific examples.

Also, I think you've missed Ptoche's point. (at least, my understanding is different from yours). The comment that "the less [the residual] the better" does not imply that its better if growth all comes from increases in the labour market. It implies that a growth accountant has done a better job if they account for a higher proportion of growth. Including education in a growth accounting model reduces the residual. This doesn't reduce the productivity of labour ("TFP"), it reduces the proportion of growth left unexplained. This is good in the sense that our understanding is improved, not in the sense that growth is more sustainable or some such.

So I understood Ptoche's comment that growth accountants love East Asia to mean that East Asian growth is easy to account for using simple accounting frameworks. Not that East Asian's are better off because they have a low residual in a growth accounting framework.

New growth theories are a step in the right direction because they begin to try to account for growth by considering more than just capital and labour growth, then calling everything else "productivity". They acknowledge (sometimes) that "productivity" is a euphemism for "I don't know" and try to find out more of what's going on. They have a lot of work still to do.

Ignoring the theoretical critique by Robinson and others(actually Wicksell noticed it much earlier) of the aggregate production function is an example of not engaging with alternative views seriously. Likewise, Phelps-Brown or Shaikh's more "numbers-oriented" critiques have also been ignored. The alternative, in my view, is to try to answer the question that TFP measurements are supposed to answer but don't, namely what is the extent of technical progress, if any. Disaggregated sectoral work by people like Howard Pack, Richard Nelson and others try to do this. This approach requires much more careful attention to data, institutions and history than a cook book growth accounting exercise. There are also multisectoral and formal modelling approaches based on this approach. I have discussed some of these and have presented a non-linear multisectoral model with multiple equilibria (and selection problems over time) in my book"Interpreting East Asian Growth and Innovation:The Future of Miracles"(Palgrave, 2004),
and in an article in Oxford Development Studies in 2002.

"So I understood Ptoche's comment that growth accountants love East Asia to mean that East Asian growth is easy to account for using simple accounting frameworks. Not that East Asian's are better off because they have a low residual in a growth accounting framework"

Thanks Dominic, that's exactly what I meant, I must say I wrote in a rather elliptic manner, as befits, it seems, blog-commenting.

I did not realize until today how active the anti- production function movement is (among Dani's readers at least). Do they have a club or something?

It all brings me back to my graduate days, when upon reading Nelson and others I asked my supervisor whether we should let go of the concept of the production function, to which he replied to the effect that "concepts don't come and go, they come and stay"

Dominic -- Yep, I was thinking more of the Asian Tigers than about China in which case it's fairly obvious and I'd have to agree...

I'm still not sure, however, how it makes economists better off to know that a set of countries had no productivity growth. Productivity growth itself should be a source of growth -- it's not merely a measure of our ignorance. And, actually, we definitely don't know that. East Asian growth accounting has not been conclusive. We can say the Solow Residual in the Asian Tigers was perhaps between -2 and 5%/annum, essentially. When countries' income grows 25 or 50-fold, as in the case of the Asian Tigers, we should not be happy when the solow residual goes to zero -- we should take that to mean we've messed up somewhere. (And, I would argue, we did.)

I would agree that the accounting of TFP is no longer enough to constitute the main body of a paper, but yet, it still is a very good introduction.

From my point of view, TFP accounting can help us identify classes of mechanisms that could be behind what we observe.

If the relative importance of TFP across countries varies consistently with the casual or empirical importance of a mechanism, that could be seen as a necessary condition for a research project on that mechanism.

I dont get the "aggregate production functions" argument. What is the alternative? One production function for each household in the economy? Every assumption is that, an assumption, the issue is whether relaxing that assumption could change the conclusion or not.

Growth accounting decompositions like gY = gA + a·gK may be useful to examine short-run dynamics. For instance, Hayashi and Prescott (2002) show that the Japanese slowdown in the 1990's was not originated in a credit crunch because the appropriate decomposition shows that it is TFP what decreases, not physical capital.

In the long-run, however, it is only technical change that matters, gY = gA/(1-a), and asserting that physical capital accumulation may account for a share of the growth rate is meaningless.

ptoche (paraphrased): "If you found it's 50% efficiency and 50% factor endowments, you can conclude that you've only done half the job."

Actually, 50% is only an upper bound on how much of the job you've done. If you are measuring capital incorrectly, or if you are using the wrong functional form of your production function, you've actually done NONE of the job.

Growth accounting is bollocks, and I'm pleased to see that I'm not the only person who noticed.

Drod: "I dont get the "aggregate production functions" argument. What is the alternative? One production function for each household in the economy? Every assumption is that, an assumption, the issue is whether relaxing that assumption could change the conclusion or not."

The point is that the legitimacy of your growth accounting rests on the legitimacy of your assumed aggregate production function, and these functions themselves are not falsifiable or testable in any way. Therefore, the problem with the misnamed TPF is deeper than "we don't know what it is"...when you "measure TPF", you haven't measured a real quantity that exists out there in the economy somewhere. TPF is dependent for its very existence on an arbitrary production function... rather than proceeding to "explain" the TPF you find, perhaps you should be "explaining" why you chose the production function that you did, or even why you think that a stable production function with assumed parameters is defenceable at all.

Demanding that someone provide an alternative to growth accounting that "does a better job" presupposes that growth accounting actually does any kind of job at all. It doesn't.

People usually say :"Seeing is believing." http://www.tt88times.com
Each attempt has a corresponding gain, in part or obvious, or vague. At least we have the kind of satisfaction After I bought this watch ,in a sense,it means a great deal to me. http://www.fashionhairfu.com

Hey very nice blog!!. Thank you for posting this, It’s just what I was browsing on bing. I’d very much rather hear opinions from an individual, rather than a corporate web page, that’s why I like blogs so much. Thanks! outstanding fantastic. Madrid Hotels

Many places and centers offer business and trade promotions to both buyers and supplier.What about the differences in skill intensities across industries? The job losses in the relatively unskilled-labor intensive battery industry should have little effect on the relatively skilled-labor intensive machinery sexshopsexyshopsexshop online

This is good site to spent time on .I just stumbled upon your informative blog and wanted to say that I have really enjoyed reading your very well written blog posts. I will be your frequent visitor, that's for sure.